OK. You may have gone down this route already. We know he died between censuses
whatever his name was, so at FreeBMD:
Search for Type: Deaths Surname: pollard First name(s): william
Start date: Mar 1841 End date: Dec 1851 District: Kingston upon Hull
Surname First name(s) Age District Vol Page
~~~~~~~~
Deaths Dec 1845 (>99%)
~~~~~~~~
POLLARD William Hull 22 261
and then:
Search for Type: Deaths Surname: bollard First name(s): william
Start date: Mar 1841 End date: Dec 1851 District: Kingston upon Hull
Sorry, we found no matches.
Looking ok so far, so that death cert could help if the name of
the informant or the address is right. Have you already looked at that one?